MATH 1131 - Calculus I

Fall 2025

Course Description & Purpose: This course is an introduction to differential and integral calculus, which is the mathematical language used in any science concerned with dynamically changing quantities. The main topics it covers are limits, derivatives, integrals, the Fundamental Theorem of Calculus, and some basic applications of these ideas.

Course Objectives: 

Successful completion of this course will require you to learn to:

1. Apply fundamental algebra skills to calculus problems.

2. Use common techniques to evaluate limits, and connect limits to derivatives.

3. Interpret derivatives as rates of change.

4. Combine ideas from algebra and trigonometry with knowledge of limits and derivatives to recognize features of the graph of a function.

5. Use derivatives to describe the features of a function and its graph, including maximum and minimum values and where they occur.

6. Identify applications of differential and integral calculus, and explain how calculus can be used in these applications.

7. Apply the Fundamental Theorem of Calculus and the substitution rule to evaluate definite and indefinite integrals.

8. Demonstrate how integrals are connected to the area under the graph of a function.